gpdCvm: Generalized Pareto Distribution Cramer-von Mises Test

In eva: Extreme Value Analysis with Goodness-of-Fit Testing

Description

Cramer-von Mises goodness-of-fit test for the Generalized Pareto (GPD) distribution.

Usage

gpdCvm(
  data,
  bootstrap = FALSE,
  bootnum = NULL,
  allowParallel = FALSE,
  numCores = 1
)

Arguments

data	Data should be in vector form, assumed to be from the GPD.
bootstrap	Should bootstrap be used to obtain p-values for the test? By default, a table of critical values is used via interpolation. See details.
bootnum	Number of bootstrap replicates.
allowParallel	Should the bootstrap procedure be run in parallel or not. Defaults to false.
numCores	If allowParallel is true, specify the number of cores to use.

Details

A table of critical values were generated via Monte Carlo simulation for shape parameters -0.5 to 1.0 by 0.1, which provides p-values via log-linear interpolation from .001 to .999. For p-values below .001, a linear equation exists by regressing -log(p-value) on the critical values for the tail of the distribution (.950 to .999 upper percentiles). This regression provides a method to extrapolate to arbitrarily small p-values.

Value

statistic	Test statistic.
p.value	P-value for the test.
theta	Estimated value of theta for the initial data.
effective_bootnum	Effective number of bootstrap replicates if bootstrap based p-value is used (only those that converged are used).

References

Choulakian, V., & Stephens, M. A. (2001). Goodness-of-fit tests for the Generalized Pareto distribution. Technometrics, 43(4), 478-484.

Examples

# Generate some data from GPD
x <- rgpd(200, loc = 0, scale = 1, shape = 0.2)
gpdCvm(x)

Example output

$statistic
[1] 0.07670005

$p.value
[1] 0.254272

$theta
    Scale     Shape 
1.0345826 0.2150924 

eva documentation built on Jan. 13, 2021, 8:34 p.m.